In a rectangle PQRS, PQ=35 cm and QR=10 cm. In what ratio does the bisector of ∠R divide PQ?
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Let X be point along SR in rectangle PQRS, where PQ=SR=40 and QR=PS=15, and all the interior angles are 90 degrees.
Triangle QRX is isosceles because angle QXR= angle RQX =90/2=45 degrees. So XR=QR=15, and SX=40-XR= 40–15=25.
Hence required ratio of SX/XR= 25/15= 5/3.
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